John Cockburn (j.cockburn@... Room E15) PHY 102: Waves & Quanta Topic 3 Energy in wave motion John Cockburn (j.cockburn@... Room E15)

Power transmitted in a wave Sinusoidal wave on a string Wave Intensity Inverse Square Law The decibel scale

Example Calculation One end of a 10m-long rope is attached to a post, and pulled taut, to a tension of 140N. If the mass of the rope is 800g, what is the speed of transverse waves on the rope? If the free end of the rope is waggled up and down with a frequency of 1.2Hz, what is the wavelength of the transverse waves on the rope?

Energy in Wave Motion Waves transport energy. Examples?? How can we quantify this??

Wave on a string A Consider force in y-direction at point A on string: Ty y Consider force in y-direction at point A on string: x

Wave on a string If a force F acts to move an object with velocity v: Rate of energy transfer (power) = F• v =Fv for F//v So for our wave on a string, P = Tyv…………….. ie Consider case for sinusoidal wave………………

Sinusoidal Wave on a string NB, for all MECHANICAL waves, Pave  A22

Example Calculation A piano wire with mass 3g and length 80cm is stretched with a tension of 25N. A wave with frequency 120Hz and amplitude 1.6mm travels along the wire. Calculate the average power carried by the wave What happens to the average power if the wave amplitude is halved?

Wave Intensity Intensity I : Average rate at which energy is transported by the wave through unit surface area perpendicular to direction of propagation (average power per unit area) For waves spreading out equally in three dimensions from a point source, the power at distance r is distributed evenly over a sphere of radius r, surface area 4r2....................

Inverse square law

Example Calculation (a) For the piano in the previous question, calculate the sound intensity at a distance of 5m (b) How much does the sound intensity decrease if you move to a distance of 15m from the piano?

The decibel scale Used to provide a logarithmic scale for comparison of 2 quantities. Often (but not only) used for sound intensities:

Examples What is the attenuation in dB of the sound intensity heard by a listener when they move from an initial distance of 3m to a final distance of 24m from the source? An electronic amplifier increases the amplitude of an AC signal from 10mV to 5V. What is the gain in dB of the amplifier?

Sound Intensities The dB scale is often used as an “absolute” measure of sound intensity (loudness) (eg the average sound intensity for traffic on the M1 is 75dB, or whatever) Here, the intensity is measured relative to the threshold of human hearing: I0 = 10-12 W/m2